"Pioneering new fields of science" isn't something humanity does very often, so you'd be hard pressed to do it alone in your retirement.
But there are LOTS of ways you can use a scientific background to advance humanity, on a limited budget. Just giving this 30 seconds of thought...
1. I know a handful of amateur astronomers who have digitized their backyard reflector telescopes and who use their home computers to scan each night's images to look for changes. These are the people who routinely discover new comets and such, or find unexplained variances in star brightness. They are part of online communities for reporting and discussing what they see.
2. People with GIS experience are in high demand in virtually every field of useful applied science. Learn to download and automate the processing of free google earth imagery. These folks find previously undiscovered archaeology sites, or track deforestation in the amazon rain forest, or the melting of greenland's ice cap.
3. More hand's on folks are currently changing the world with consumer grade electronics. Spend a month watching maker videos on youtube, learn to program a raspberry pi, and you can design and manufacturer your own smart_whatever hardware. Just look at the explosive growth in smart home technology, the field of wireless connectivity and phone integration is ripe to upset a hundred different established industries. With cheap ministick computers plus a sub-$1000 3D printer and you can reproduce thirty different startups already valued at >$1million.
4. Apply technologies that are currently research experiments to residential use. Read up on algal biofuels and then build a reactor in your back yard, build a methane digester to go with it, figure out how to integrate the two and make it cheap and reproducible and you'll have thousands of people building them.
5. Unprofitable genetics. Seriously, for about $15k in laboratory equipment you can do basic genetics research in your kitchen, of the type that nobody else is doing because there's no money in it. We have fifty labs working on how to make photosynthesis more efficient, and nobody at all working on why wiener dogs have short legs. That person could be you, for six months worth of work. Or if you're the evil type, you can weaponize influenza and wipe out half of the planet's population. Nothing says "going down in history" quite like "evil genius who started a global pandemic". So easy an undergrad could do it!
There are huge amounts of unanalyzed data available to the public, waiting for the right person to come along and dig into it. Each year the google science fair
produces at least three or four potentially world-altering technologies that some high school kid came up with on a shoestring budget. You can do that, too. It's not "pioneering new fields of science" but it is making a difference.